Final answer:
To find the velocity of projection, we can use the equations of projectile motion. The range and maximum height of the projectile are given, and we can solve for the velocity using these values and the other known variables.
Step-by-step explanation:
Given the values of range and maximum height of a projectile, we can use the equations of projectile motion to find the velocity of projection. The range of a projectile is given by:
R = (v^2 * sin(2θ)) / g
where R is the range, v is the velocity of projection, θ is the angle of projection, and g is the acceleration due to gravity. The maximum height is given by:
H = (v^2 * sin^2(θ)) / (2 * g)
Combining these equations, we have:
(v^2 * sin(2θ)) / g = 12
(v^2 * sin^2(θ)) / (2 * g) = 4
Solving these equations will give us the value of v, which represents the velocity of projection.